{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:O33SJRXTUTF67C4V3AP5HYQ3VN","short_pith_number":"pith:O33SJRXT","canonical_record":{"source":{"id":"1411.6476","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-11-24T14:59:42Z","cross_cats_sorted":[],"title_canon_sha256":"a3b50683b03c87a6e102f11a0ddcdc904f04603c5ab85ad37346dd7c97b933c8","abstract_canon_sha256":"d8dd4075bb4b2988e892804ebfeb5ded84f1f5794dba769099d2a54963008dfe"},"schema_version":"1.0"},"canonical_sha256":"76f724c6f3a4cbef8b95d81fd3e21bab40114638cd4c33685ffb968f94d931b0","source":{"kind":"arxiv","id":"1411.6476","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.6476","created_at":"2026-05-18T01:19:12Z"},{"alias_kind":"arxiv_version","alias_value":"1411.6476v3","created_at":"2026-05-18T01:19:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.6476","created_at":"2026-05-18T01:19:12Z"},{"alias_kind":"pith_short_12","alias_value":"O33SJRXTUTF6","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"O33SJRXTUTF67C4V","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"O33SJRXT","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:O33SJRXTUTF67C4V3AP5HYQ3VN","target":"record","payload":{"canonical_record":{"source":{"id":"1411.6476","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-11-24T14:59:42Z","cross_cats_sorted":[],"title_canon_sha256":"a3b50683b03c87a6e102f11a0ddcdc904f04603c5ab85ad37346dd7c97b933c8","abstract_canon_sha256":"d8dd4075bb4b2988e892804ebfeb5ded84f1f5794dba769099d2a54963008dfe"},"schema_version":"1.0"},"canonical_sha256":"76f724c6f3a4cbef8b95d81fd3e21bab40114638cd4c33685ffb968f94d931b0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:12.501609Z","signature_b64":"LknxYDS6ca6vztFb1UE9Lq6K+U4bgZQm+Db95t8tHBV9l3UpYw9lEaJtNej6gT4+vrlfF54bPAFCzrTcch2DBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"76f724c6f3a4cbef8b95d81fd3e21bab40114638cd4c33685ffb968f94d931b0","last_reissued_at":"2026-05-18T01:19:12.500962Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:12.500962Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.6476","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:19:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/43nbHAyoke5nEEO2vIyoW98Mh38VSIIR5HCv7eP+Ika1ACuRVEXe9ygSiomacLBwZa0OBzjkeoMDa9eHAxeAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T01:17:44.484809Z"},"content_sha256":"a2b49d1acad61361fc54f864e899d94565c7754034081f357ca28625563fee05","schema_version":"1.0","event_id":"sha256:a2b49d1acad61361fc54f864e899d94565c7754034081f357ca28625563fee05"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:O33SJRXTUTF67C4V3AP5HYQ3VN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weak error analysis for semilinear stochastic Volterra equations with additive noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Adam Andersson, Mih\\'aly Kov\\'acs, Stig Larsson","submitted_at":"2014-11-24T14:59:42Z","abstract_excerpt":"We prove a weak error estimate for the approximation in space and time of a semilinear stochastic Volterra integro-differential equation driven by additive space-time Gaussian noise. We treat this equation in an abstract framework, in which parabolic stochastic partial differential equations are also included as a special case. The approximation in space is performed by a standard finite element method and in time by an implicit Euler method combined with a convolution quadrature. The weak rate of convergence is proved to be twice the strong rate, as expected. Our convergence result concerns n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.6476","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:19:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QWR31ZX0zfONGQAUhw+uSp+9BveEQFmFdCqMniAh9zPtgwUGERlzRT2LcPkhoZAXX2lbfaH6A6FiH+mcybxiDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T01:17:44.485523Z"},"content_sha256":"8f8cf4bebb0e862cd9b119ae9118be2eaadbb62bc78fff4c3462de40bcfd783e","schema_version":"1.0","event_id":"sha256:8f8cf4bebb0e862cd9b119ae9118be2eaadbb62bc78fff4c3462de40bcfd783e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O33SJRXTUTF67C4V3AP5HYQ3VN/bundle.json","state_url":"https://pith.science/pith/O33SJRXTUTF67C4V3AP5HYQ3VN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O33SJRXTUTF67C4V3AP5HYQ3VN/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-08T01:17:44Z","links":{"resolver":"https://pith.science/pith/O33SJRXTUTF67C4V3AP5HYQ3VN","bundle":"https://pith.science/pith/O33SJRXTUTF67C4V3AP5HYQ3VN/bundle.json","state":"https://pith.science/pith/O33SJRXTUTF67C4V3AP5HYQ3VN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O33SJRXTUTF67C4V3AP5HYQ3VN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:O33SJRXTUTF67C4V3AP5HYQ3VN","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"d8dd4075bb4b2988e892804ebfeb5ded84f1f5794dba769099d2a54963008dfe","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-11-24T14:59:42Z","title_canon_sha256":"a3b50683b03c87a6e102f11a0ddcdc904f04603c5ab85ad37346dd7c97b933c8"},"schema_version":"1.0","source":{"id":"1411.6476","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.6476","created_at":"2026-05-18T01:19:12Z"},{"alias_kind":"arxiv_version","alias_value":"1411.6476v3","created_at":"2026-05-18T01:19:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.6476","created_at":"2026-05-18T01:19:12Z"},{"alias_kind":"pith_short_12","alias_value":"O33SJRXTUTF6","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"O33SJRXTUTF67C4V","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"O33SJRXT","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:8f8cf4bebb0e862cd9b119ae9118be2eaadbb62bc78fff4c3462de40bcfd783e","target":"graph","created_at":"2026-05-18T01:19:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We prove a weak error estimate for the approximation in space and time of a semilinear stochastic Volterra integro-differential equation driven by additive space-time Gaussian noise. We treat this equation in an abstract framework, in which parabolic stochastic partial differential equations are also included as a special case. The approximation in space is performed by a standard finite element method and in time by an implicit Euler method combined with a convolution quadrature. The weak rate of convergence is proved to be twice the strong rate, as expected. Our convergence result concerns n","authors_text":"Adam Andersson, Mih\\'aly Kov\\'acs, Stig Larsson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-11-24T14:59:42Z","title":"Weak error analysis for semilinear stochastic Volterra equations with additive noise"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.6476","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:a2b49d1acad61361fc54f864e899d94565c7754034081f357ca28625563fee05","target":"record","created_at":"2026-05-18T01:19:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"d8dd4075bb4b2988e892804ebfeb5ded84f1f5794dba769099d2a54963008dfe","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-11-24T14:59:42Z","title_canon_sha256":"a3b50683b03c87a6e102f11a0ddcdc904f04603c5ab85ad37346dd7c97b933c8"},"schema_version":"1.0","source":{"id":"1411.6476","kind":"arxiv","version":3}},"canonical_sha256":"76f724c6f3a4cbef8b95d81fd3e21bab40114638cd4c33685ffb968f94d931b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"76f724c6f3a4cbef8b95d81fd3e21bab40114638cd4c33685ffb968f94d931b0","first_computed_at":"2026-05-18T01:19:12.500962Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:12.500962Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LknxYDS6ca6vztFb1UE9Lq6K+U4bgZQm+Db95t8tHBV9l3UpYw9lEaJtNej6gT4+vrlfF54bPAFCzrTcch2DBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:12.501609Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.6476","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2b49d1acad61361fc54f864e899d94565c7754034081f357ca28625563fee05","sha256:8f8cf4bebb0e862cd9b119ae9118be2eaadbb62bc78fff4c3462de40bcfd783e"],"state_sha256":"718be6772e2d4d2944ec74cdc7bd290cf06a0dd5cb187fe0890f9c6d952caa4b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4ZwNrdFnFccj6IZ61+P8j0mIzNqHnxP3M9MLTZj8zppDz+UZpG1mUeSvvdiUSzfhlfUjhOCWY/P+mKKLvZpKDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T01:17:44.489825Z","bundle_sha256":"28811c383e139e8fac5f1f09b8dfb14921ffea15df5241629b8e6683b9517b22"}}